The result of a hypothesis test is a probability of the form:
\[ \mathbb{P}(\textrm{ data or more extreme } | \ H_0 \textrm{ true }) \]
while most people think they're getting
\[ \mathbb{P}(\ H_0 \textrm{ true } | \textrm{ data or more extreme}) \]
How can we go from the former to the latter?